Comparison of identification and control of 2 axes pam manipulator

공학박사 학위논문 축 공압 인공근육 매니퓰레이터의 추정 및 제어에 관한 비교 연구 Comparison of Identification and Control of 2-Axes PAM Manipulator 울산대학교 대학원 기계자동차 공학부 Ho Pham Huy Anh 축 공압 인공근육 매니퓰레이터의 추정 및 제어에 관한 비교 연구 Comparison of Identification and Control of 2-Axes PAM Manipulator 지도교수 안경관 이 논문을공학박사학위 논문으로 제출함 2008 년 11 월 울산대학교 대학원 기계자동차 공학부 Ho Pham Huy Anh ii Ho Pham Huy Anh 의 공학박사 학위 논문을 인준함 심사위원장 이병룡 (인) 심사위원 양순용 (인) 심사위원 하철근 (인) 심사위원 박중호 (인) 심사위원 안경관 (인) 울산대학교 대학원 기계자동차 공학부 2008 년 11 월 Thesis for the Degree of Doctor of Philosophy Comparison of Identification and Control of 2-Axes PAM Manipulator By Ho Pham Huy Anh Advisor: Prof KYOUNG KWAN AHN School of Mechanical and Automotive Engineering Graduate School University of ULSAN November 2008 Comparison of Identification and Control of 2-Axes PAM Manipulator By Ho Pham Huy Anh Advisor: Prof KYOUNG KWAN AHN Submitted to the School of Mechanical and Automotive Engineering in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy At Graduate School, University of ULSAN November 2008 ii Comparison of Identification and Control of 2-Axes PAM Manipulator A Dissertation By Ho Pham Huy Anh Approved of styles and contents by: Chairman BYUNG RYONG LEE Advisor KYOUNG KWAN AHN Member SOON YOUNG YANG Member CHEOL GEUN HA Member JUNG HO PARK November 2008 iii Acknowledgments This thesis would not have been completed without the help and unlimited support from professors, colleagues, friends, and my love-family from whom I receive the encouragement, the opportunity, the confidence and by so to whom I want to dedicate my best grateful Firstly, I want to express my sincere gratitude to my advisor, Prof Kyoung Kwan Ahn, for all of his guidance, advice and support during the course of my research and thesis writing Forever I will remember the opportunities he has provided me, for his constant support and his initiative ideas and suggestions My respect for him will always be in my mind I am also honored to have Prof Byung Ryong Lee, Prof Soon Young Yang, Prof Cheol Geun Ha and Prof Jung Ho Park in my committee, whose inspiration, support and perseverance made this dissertation become possible I would like to thank them for their interest and encouragement throughout this research No words for me to express my sincere gratitude towards all my Korean, Bangaldesh and Vietnamese friends (Thanh-Hon-Nam-Hao-Kha-Tu-Truong-Hanh-Hung-JongIl-Amin-Mafuz and others) Not much happy people like me to have their best friend Thanks for helping me to pass through difficult moments, for yours deep thinking and yours contributions to the realization of my thesis, and especially for the many animated discussions on the subject This thesis is dedicated to my darling wife Le Tan Loi, my sons Bim-Bum and my girl Bo Special sentiment is also expressed to my sisters, my brother Huy Don and their family for taking care of me during the time I studied abroad Finally I dedicate this work to my father and my late mother Their endless love for me always supports me in all my life November 2008 Ho Pham Huy Anh iv Contents Acknowledgments iv Contents v List of Figures vii List of Tables xi Nomenclatures xii Abstract xiii Part I: Introduction Introduction 1.1 Overview 1.2 Motivation 1.3 Outline of Thesis Configuration, experiment setup and characteristic of pneumatic artificial muscle (PAM) manipulator 10 2.1 Introduction 10 2.2 Configuration, experiment setup and characteristic of 2-axes PAM manipulator 11 2.2.1 Configuration of 2-axes PAM manipulator system 11 2.2.2 Experiment setup 12 2.2.3 Configuration of 1-axes PAM manipulator system 14 2.2.4 Basic characteristic of PAM manipulator 16 Part II: Intelligent Models and Model-Based Advanced Control Schemes of 2-Axes PAM Manipulator Modeling and Control of the 1-Axes PAM Manipulator using MGA-based NARX Fuzzy model 22 3.1 Introduction 22 3.2 Modified genetic algorithm (MGA) for NARX fuzzy model Identification 23 3.2.1 Conventional genetic algorithm (GA) 23 3.2.2 Modifications to genetic algorithm (MGA) 24 3.2.3 Modified genetic algorithm (MGA) for optimizing fuzzy model’s parameters 27 3.3 MGA-based PAM manipulator NARX fuzzy model identification 31 3.4 Configuration of PAM manipulator system and PRBS training data 33 3.5 Design and Implementation of MGA-based NARX fuzzy model 35 3.6 Results of MGA-based PAM manipulator NARX fuzzy model identification 40 3.6.1 GA-based PAM manipulator TS fuzzy model identification 40 3.6.2 MGA-based PAM manipulator TS fuzzy model identification 44 3.6.3 MGA-based PAM manipulator NARX fuzzy model identification 49 3.7 20 Conclusion 60 Modeling and Model-based Control of 1-Axes PAM Manipulator using Neural NARX model v 62 4.1 Introduction 62 4.2 Modeling of 1-Axes PAM manipulator using neural NARX model and INCBP algorithm 63 4.2.1 Recurrent neural NARX model and Back-Propagation (BP) learning algorithm 63 4.2.2 INCBP learning algorithm of Neural NARX model identification 68 4.2.3 Modeling of PAM manipulator Neural NARX model 70 4.3 Experimental results 72 4.4 Advanced Control of PAM manipulator based on neural NARX model 88 4.4.1 PAM manipulator forward and inverse neural NARX model identification 89 4.4.2 Proposed Hybrid Neural NARX Internal Model (NARX-IMC-PID) Control 95 4.4.3 Experimental results 98 4.5 108 Modeling and Control of 2-Axes PAM Manipulator using MGA-based Double NARX fuzzy model 109 5.1 Introduction 109 5.2 Modified genetic algorithm (MGA) for NARX fuzzy model Identification 110 5.3 Identification of 2-axes PAM manipulator based on Double NARX fuzzy model 111 5.4 Identification of Inverse and Forward Double NARX fuzzy model 115 5.5 Experimental results 120 5.5.1 Identification of 2-axes PAM manipulator Forward Double NARX fuzzy model 120 5.5.2 Identification of 2-axes PAM manipulator Inverse Double NARX fuzzy model 5.6 5.7 Conclusion 124 5.6.1 Implementation of MGA-based inverse NARX fuzzy model 125 5.6.2 Results of MGA-based Inverse NARX Fuzzy model Identification 126 5.6.3 Hybrid Online DNN-PID Feed-forward Inverse NARX Fuzzy Control scheme 130 5.6.4 Experimental results 135 Conclusion 143 Modeling and Control of 2-Axes PAM Manipulator using Neural MIMO NARX model 144 6.1 Introduction 144 6.2 Proposed MIMO Neural NARX model and BP learning algorithm 145 6.3 Identification of Inverse and Forward Neural MIMO NARX model 147 6.4 Proposed Hybrid online neural MIMO NARX Feed-forward PID control system 155 6.4.1 Controller design 155 6.4.2 Experiment setup 158 6.4.3 Experimental results 158 6.5 Conclusion 170 Part IV: Conclusion and discussion 122 Advanced Control of PAM manipulator based on Inverse NARX Fuzzy model 172 Conclusion and discussion 173 References 177 Publications 184 vi List of Figures Figure 2.1 Structure of the PAM 11 (a) Working of PAM (b) PAM – FESTO Product (c) The structure of PAM Figure 2.2 General configuration of 2-axes PAM manipulator 12 Figure 2.3: Working principle of the 2-axes PAM manipulator 12 Figure 2.4a Schematic diagram of the 2-axes PAM manipulator 13 Figure 2.4b Experimental Configuration of the 2-axes PAM manipulator system 14 Figure 2.5 Block diagram for obtaining PRBS input-output data of the 1-link PAM manipulator 15 Figure 2.6 Block diagram of the experimental apparatus of the 1-link PAM manipulator 16 Figure 2.7 Basis Characteristics of the PAM 17 Figure 2.8 Hysteresis of the PAM 18 Figure 2.9 h -F relationships of artificial muscle (extracted from (FESTO, 2005) [29] ) 18 Figure 3.1: The flow chart of conventional GA optimization procedure 25 Figure 3.2: The flow chart of Modified MGA optimization procedure 30 Figure 3.3 Procedure of the PAM manipulator NARX Fuzzy Model Identification 30 Figure 3.4a Block diagram of The MGA-based PAM manipulator’s TS Fuzzy Model Identification 32 Figure 3.4b Block diagram of The MGA-based PAM manipulator’s NARX11 Fuzzy Model Identification 32 Figure 3.4c Block diagram of The MGA-based PAM manipulator’s NARX22 Fuzzy Model Identification 33 Figure 3.5 Experiment data obtained from the PAM manipulator 34 Figure 3.6a Training data obtained from the PAM manipulator 34 Figure 3.6b Validating data obtained from the PAM manipulator 34 Figure 3.7 Validating pseudo-PRBS data obtained from the PAM manipulator 35 Figure 3.8 Triangle input membership function with spacing factor = 36 Figure 3.9a The Seed Points and the Grid Points for Rule-Base Construction 37 Figure 3.9b Derived Rule Base 37 Figure 3.10 Fitness Convergence GA-based Fuzzy Model Identification of the PAM manipulator 40 Figure 3.11a Estimation of GA-based Fuzzy Model of the PAM manipulator 41 Figure 3.11b Validation of GA-based Fuzzy Model of the PAM manipulator 41 Figure 3.11c Membership Input-Output & Surf-Viewer of GA-based Fuzzy Model Identification 42 Figure 3.11d Convergence of Principal Parameters of GA-based Fuzzy Model Identification 43 Figure 3.12 Fitness Convergence MGA-based Fuzzy Model Identification of the PAM manipulator 45 Figure 3.13a Membership Input-Output & Surf-Viewer of MGA-based Fuzzy Model Identification 46 Figure 3.13b Estimation of MGA-based TS Fuzzy Model of the PAM manipulator 47 Figure 3.13c Validation of MGA-based TS Fuzzy Model of the PAM manipulator 47 Figure 3.13d Convergence of principal parameters of the MGA-based Fuzzy Model of the PAM manipulator 48 Figure 3.14 Fitness Convergence MGA-based NARX11 Fuzzy Model Identification of the PAM manipulator 50 Figure 3.15a Membership Input-Output & Surf-Viewer of MGA-based NARX11 Fuzzy Model Identification 51 Figure 3.15b Estimation of MGA-based NARX11 Fuzzy Model of the PAM manipulator 52 Figure 3.15c Validation of MGA-based NARX11Fuzzy Model of the PAM manipulator 52 vii CH6-Modeling & Model-based Advanced Control of 2-Axes PAM Manipulator using Neural MIMO NARX Model 171 model continues to be applied to enhance the control performance of the 2-axes PAM manipulator, due to the extraordinary capacity in learning such coupled effect and nonlinear characteristic Results of training and testing on the complex dynamic systems such as the 2axes PAM manipulator show that the newly proposed MIMO NARX model presented in this study can be used in online control with better dynamic property and strong robustness Likewise, the proposed Hybrid Neural MIMO NARX FNN-PID Control scheme is quite suitable to be applied for the modeling, identification and control of various plants, including highly nonlinear MIMO system without regard greatly changing external environments and nonlinear dynamic coupled effect as well As with the conclusions, this chapter proposes the new concept of neural MIMO NARX model that guarantees for improvement intelligent neural MIMO NARX11 and neural MIMO NARX22 models as well as intelligent model–based Hybrid Neural MIMO NARX FNN-PID control schemes for 2-axes PAM manipulator as to realize the human friendly elbow and wrist rehabilitation PAM-based robot in near future Part III Conclusion and Discussion 173 CH7- Conclusion and Discussion Chapter Conclusion and Discussion This thesis addresses the innovative of intelligent modeling and identification of highly nonlinear 2-axes PAM manipulator system in order to realize the human friendly therapy robot in the near future The novel proposed intelligent models are designed for modeling and control the 1-axis and 2-axes PAM manipulator system with the best performance without regard external inertia load, tracking error to zeros as fast as possible regardless the changes of load condition or contact force variations Consequently, intelligent model-based advanced position control schemes obtain not only the high accuracy but also the perfect robustness with the load condition changes up to 2000% In summary the thesis concludes with novel results as follows: To propose a novel modified genetic algorithm (MGA) for identifying a newly intelligent NARX fuzzy model of nonlinear PAM manipulator system which adapts to the changes of external Load up to 2000% (from 0.5[kg] to 10[kg]) To propose an advanced Incremental Back-Propagation (INCBP) learning algorithm for training a novel proposed neural NARX model of dynamic PAM manipulator which is applied successfully in novel Hybrid online neural FNN-NARX PID position control To improve a newly intelligent Double NARX Fuzzy model well adapting to highly nonlinear coupled effects of the 2-axes PAM manipulator system To offer an intelligent neural MIMO NARX Feed-forward PID control based on novel proposed inverse neural MIMO NARX model used in trajectory tracking control To develop an intelligent Hybrid PID neural NARX Internal Model Control (IMC) based on novel proposed inverse and forward neural NARX model used in the PAM manipulator system position control To develop and implement an innovative intelligent gain scheduling adaptive control using inverse NARX fuzzy model, neural PID and genetic algorithm which obtains the excellent performance on PAM manipulator system position control CH7- Conclusion and Discussion 174 without regard the various frequencies of sine and cosine reference for each joint of PAM system To propose and develop an advanced Hybrid online neural MIMO NARX Feedforward PID control applied successfully in 2-axes PAM manipulator system trajectory control which is well fit as one of the most effective control methods to develop a practically available human friendly medical robot using the 2-axes PAM manipulator system To achieve the objectives and goals above, the novel proposed intelligent models as well as intelligent model-based advanced controllers have been innovated and are described specifically in each chapter as follows: The Chapter investigates the technique of the modeling and identification a new dynamic NARX fuzzy model by means of genetic algorithms In conventional identification techniques, difficulties such as poor knowledge of the process, inaccurate process or complexity of the resulting mathematical model, all which limit their usefulness during dealing with dynamic nonlinear industrial processes To overcome these difficulties, this Chapter proposes a novel approach by using a modified genetic algorithm (MGA) combined with the powerful predictive capability of nonlinear ARX (NARX) model for generating the dynamic NARX Takagi-Sugeno (TS) Fuzzy model MGA algorithm processes the experimental input-output training data from the real PAM system and optimizes the NARX fuzzy model parameters This is referred to perform fuzzy identification by which automatically generates the appropriate fuzzy ifthen rules to characterize the dynamic nonlinear features of the real plant The prototype pneumatic artificial muscle (PAM) manipulator system, being a typical nonlinear and time-varying system is used as a test system for this novel approach The results prove that, with this MGA-based intelligent modeling and identification, the novel NARX Fuzzy model identification approach of the prototype PAM manipulator system achieved highly outstanding performance and high accuracy as well In Chapter 4, a PAM manipulator system is dynamically modeled through a neural NARX model-based modeling and identification using experimental input-output training data The proposed incremental back propagation (INCBP) learning algorithm which yields faster convergence than conventional back propagation (BP) algorithm is CH7- Conclusion and Discussion 175 applied to train the weights of proposed neural NARX model The evaluation of different nonlinear Neural Network Auto-Regressive with eXogenous input (NARX) models of PAM manipulator system with various input nodes as well as various hidden layer nodes is discussed For the first time, the nonlinear Neural NARX model of the dynamic PAM manipulator system has been investigated The results show that the nonlinear Neural NARX model trained by INCBP yields better performance and higher accuracy than the traditional linear ARX model These results can be applied in modeling, identifying and controlling as well not only of the PAM manipulator system but also of other highly nonlinear systems Forwardly, as to demonstrate the power of proposed neural NARX model, it introduces a novel technique of the hybrid internal model control (IMC) – error feedback PID control scheme for the adaptive tracking of a wide range of nonlinear dynamic plants based on proposed neural NARX model The overall control scheme combines the robust IMC structure wherein inverse and forward internal models based on offline training nonlinear neural NARX models with feedback PID regulator The effectiveness of the proposed adaptive control scheme is demonstrated through real-time applications to a pneumatic artificial muscle (PAM) manipulator system position control which will be applied as an elbow and wrist rehabilitation device in near future The experiments are carried on with four different conditions of payload and three kinds of control methods From these experimental results, it is determined that the proposed nonlinear hybrid IMC-NARX-PID controller based on neural NARX model is one of the most effective methods to develop a practically available human friendly PAM-based therapy robot in the near future In Chapter 5, a nonlinear Double NARX fuzzy model is used for simultaneously modeling and identifying both joints of the prototype 2-axes PAM manipulator system The highly nonlinear coupling features of both joints of the 2-axes PAM manipulator system are modeled thoroughly through a Double NARX Fuzzy Model-based identification process based on appropriate experimental input-output training data The evaluation of different nonlinear Double NARX Fuzzy Models of the 2-axes PAM manipulator system with various ARX model structures will be discussed For first time, the nonlinear Double NARX Fuzzy Model scheme of the prototype 2-axes PAM manipulator system has been investigated The results show that the nonlinear Double NARX Fuzzy Model trained by modified genetic algorithm yields more performance and higher accuracy than traditional Fuzzy model CH7- Conclusion and Discussion 176 Forwardly, as to assert the potentiality of proposed NARX fuzzy model, a new model-based control algorithm is firstly proposed with a gain scheduling adaptive control scheme based on inverse NARX fuzzy model, neural dynamic PID and genetic algorithms An inverse NARX fuzzy feed-forward controller is developed, which is an optimal discrete time version of the conventional feed-forward control one The newly Inverse NARX fuzzy model structure is optimally designed by using a modified genetic algorithm (MGA) for simultaneously satisfying not only the accuracy but also the robustness specifications Hence, from which results an optimal Inverse NARX fuzzy feed-forward controller Furthermore, a neural gain scheduler is designed and online updated by the fast learning Back-Propagation (FLBP) algorithm Simultaneously, FLBP algorithm will tune online the optimal parameters of the neural dynamic PID controller in parallel operation with the inverse NARX fuzzy model-based feed-forward controller Experimental results demonstrate the efficiency of proposed model-based control applied on 2-axes PAM manipulator system trajectory control In Chapter 6, a new approach of Neural MIMO NARX model, firstly utilized in simultaneous modeling and identification two-joint’s dynamics of the prototype 2-axes pneumatic artificial muscle (PAM) manipulator system system Forwardly, base on the resulting Inverse Neural MIMO NARX model, a novel Hybrid MIMO NARX modelbased feed-forward PID control scheme is applied to control the position of the highly nonlinear 2-axes PAM manipulator system as to improve its joint angle position output performance The experimental investigation of novel proposed control scheme is carried out on the 2-axes PAM manipulator system with different end-point Payload values and using three different control methods (PID, proposed MIMO NARX11FNN-PID and proposed MIMO NARX22-FNN-PID control respectively) as to 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(2002), 343-354 [77] Hu, S., Ang, M and Krishnan, H., On-line Neural Network Compensator for Constrained Robot Manipulators, In Proc of the 3rd Asian Control Conference, Shanghai, (2000), 1621-1627 [78] Sun, W and Wang, Y., A Recurrent Fuzzy Neural Network Based Adaptive Control and its Application on Robotic Tracking Control, Neural Information Processing-Letters and Reviews, Vol 5, No 1, (2004), 19-26 Publications and Conferences Ho Pham Huy Anh School of Mechanical and Automotive Engineering University of Ulsan, Korea A International Journals [1] Ahn, K.K and Anh, H.P.H., 2007, “A New Approach of Modeling and Identification of the Pneumatic Artificial Muscle (PAM) Manipulator Based on Recurrent Neural Networks” JSCE International Journal of System and Control Engineering, Proceedings of the IMechE, Part I, Sep 2007, 221(I8), pp 1101-1122 (SCI – Accepted & Published) [2] Ahn, K.K and Anh, H.P.H., 2007, “Comparative Study of Modeling and Identification of the Pneumatic Artificial Muscle (PAM) Manipulator Using Recurrent Neural Networks,” Journal of Mechanical Science and Technology (KSME), Vol.22, No.7 (2008), pp 1287-1299 (SCIE – Accepted & Published) [3] Ahn, K.K and Anh, H.P.H., 2007, “Identification of the pneumatic artificial muscle manipulators by MGA-based nonlinear NARX fuzzy model,” submitted to International Journal of MECHATRONICS (SCI - Accepted & Published) [4] Ahn, K.K and Anh, H.P.H., 2008, “Modeling Identification and Advanced Feedforward PID Control of The Nonlinear 2-Axes Pneumatic Artificial Muscle (PAM) Robot Arm Using MIMO Recurrent Neural Networks” submitted to JSCE International Journal of System and Control Engineering, Proceedings of the IMEchE (SCI - In resubmission) [5] Ahn, K.K and Anh, H.P.H., 2008, “Design and Implementation an Adaptive Recurrent Neural Networks (ARNN) Controller of the Pneumatic Artificial Muscle (PAM) Manipulator,” submitted to International Journal of MECHATRONICS (SCI - In revision) [6] Ahn, K.K and Anh, H.P.H., 2008, “A New Approach of Modeling Identification and Hybrid Feed-Forward-PID Control of The Pneumatic Artificial Muscle (PAM) Robot Publications and Conferences 184 Arm using Inverse NARX Fuzzy Model and Genetic Algorithm,” submitted to International Journal of Engineering Applications of Artificial Intelligence, Proceedings of the EAAI (SCI - In revision) [7] Ahn, K.K and Anh, H.P.H., 2008, “Inverse Model Identification of 2-Axes PAM Robot Arm Using Double NARX Fuzzy Model and Genetic Algorithm,” submitted to IEEE/ASME Transactions on MECHATRONICS (SCI - In revision) B International Conference Papers [1] Ahn, K.K and Anh, H.P.H., 2005, “An approach for effectively convergent optimization of genetic algorithm by applying a new acceleration technique,” in Proc ISEE-2005 Int Conf., IHUT, HCM City, Viet Nam (Accepted) [2] Ahn, K.K and Anh, H.P.H., 2005, “Using a modified genetic algorithm for multiobjective modeling and optimization a Takagi-Sugeno fuzzy model,” in Proc ISEE2005 Int Conf., IHUT, HCM City, Viet Nam (Accepted) [3] Ahn, K.K and Anh, H.P.H., 2006, “Design & Implementation an Adaptive TakagiSugeno fuzzy neural networks controller for the two-links pneumatic artificial muscle (PAM) manipulator using in elbow rehabilitation,” in Proc., IEEE-ICCE2006 Int., Conf., HUT06, Hanoi, VN, Vol 1, pp 76~81 (Accepted) [4] Ahn, K.K and Anh, H.P.H., 2006, “System modeling and identification the two-link pneumatic artificial muscle (PAM) manipulator optimized with genetic algorithm,” in Proc., IEEE-ICASE2006 Int., Conf., Busan, Korea (Accepted) [5] Ahn, K.K and Anh, H.P.H., 2007, “System Modeling Identification and Control of the 2-Link Pneumatic Artificial Muscle (PAM) Manipulator Optimized with Genetic Algorithm,” in IEEE-ICCAS-2007 Int., Conf., Control, Automation and Systems, Guangzhou, China (Accepted) Publications and Conferences 185 [6] Ahn, K.K and Anh, H.P.H., 2007, “A Comparative Study of Modeling and Identification of the Pneumatic Artificial Muscle (PAM) Manipulator based on Recurrent Neural Networks,” in Proc ISEE-2007 Int Conf., HUT, HCM City, Viet Nam (Accepted) [7] Ahn, K.K and Anh, H.P.H., 2007, “Neural NNARX model identification of PAMbased Robot Arm using Recurrent Neural Networks and Genetic Algorithm,” in Proc., ISEE2007 Int Conf., HUT, HCM City, Viet Nam (Accepted) [8] Ahn, K.K and Anh, H.P.H., 2007, “A New MIMO Approach of Modeling and Identification of Pneumatic Artificial Muscle (PAM) Manipulator Using Recurrent Neural Networks,” in Proc., ICMT Int Conf Mechatronics Technology, Ulsan, Korea (Accepted) [9] Ahn, K.K., Anh, H.P.H and Yoon J.I., 2008, “Neural NARX model identification of PAM-based Robot Arm using Recurrent Neural Networks and Genetic Algorithm,” in Proc., IEEE-ICSMA2008 Int Conf., Seoul, Korea (Accepted) [10] Ahn, K.K., Anh, H.P.H and Yoon J.I., 2008, “A New MIMO Approach of Modeling and Identification of Pneumatic Artificial Muscle (PAM) Manipulator Using Recurrent Neural Networks,” in Proc., IEEE-ICCE08 Int., Conf., Hoi An, Viet Nam (Accepted) ... characteristic of 2- axes PAM manipulator 11 2. 2.1 Configuration of 2- axes PAM manipulator system 11 2. 2 .2 Experiment setup 12 2 .2. 3 Configuration of 1 -axes PAM manipulator system 14 2. 2.4 Basic characteristic... Figure 2. 2 General configuration of 2- axes PAM manipulator 12 Figure 2. 3: Working principle of the 2- axes PAM manipulator 12 Figure 2. 4a Schematic diagram of the 2- axes PAM manipulator 13 Figure 2. 4b... 4 .20 Comparison of PAM manipulator and Neural NARX33 Model response 85 Figure 4 .21 Comparison of PAM manipulator and Neural NARX 22 Model response (BP method & hidden nodes) 86 Figure 4 .22 Comparison